Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9408,2,Mod(1,9408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9408, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9408.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9408.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(75.1232582216\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9408.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.585786 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843 | 1.45583 | 0.727913 | − | 0.685670i | \(-0.240491\pi\) | ||||
0.727913 | + | 0.685670i | \(0.240491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.58579 | 1.11222 | 0.556108 | − | 0.831110i | \(-0.312294\pi\) | ||||
0.556108 | + | 0.831110i | \(0.312294\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.17157 | −0.268777 | −0.134389 | − | 0.990929i | \(-0.542907\pi\) | ||||
−0.134389 | + | 0.990929i | \(0.542907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.82843 | 0.508001 | 0.254000 | − | 0.967204i | \(-0.418254\pi\) | ||||
0.254000 | + | 0.967204i | \(0.418254\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.82843 | 0.840521 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.65685 | −1.58758 | −0.793789 | − | 0.608194i | \(-0.791894\pi\) | ||||
−0.793789 | + | 0.608194i | \(0.791894\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.24264 | −0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.75736 | 0.274453 | 0.137227 | − | 0.990540i | \(-0.456181\pi\) | ||||
0.137227 | + | 0.990540i | \(0.456181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.3137 | −1.72532 | −0.862662 | − | 0.505781i | \(-0.831205\pi\) | ||||
−0.862662 | + | 0.505781i | \(0.831205\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.585786 | −0.0873239 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4853 | 1.82117 | 0.910583 | − | 0.413327i | \(-0.135633\pi\) | ||||
0.910583 | + | 0.413327i | \(0.135633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.58579 | 0.642139 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.82843 | −0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.17157 | −0.155179 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.48528 | 1.10469 | 0.552345 | − | 0.833616i | \(-0.313733\pi\) | ||||
0.552345 | + | 0.833616i | \(0.313733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.07107 | 0.393210 | 0.196605 | − | 0.980483i | \(-0.437008\pi\) | ||||
0.196605 | + | 0.980483i | \(0.437008\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.48528 | 0.308261 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3137 | 1.38219 | 0.691095 | − | 0.722764i | \(-0.257129\pi\) | ||||
0.691095 | + | 0.722764i | \(0.257129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.48528 | 0.769661 | 0.384831 | − | 0.922987i | \(-0.374260\pi\) | ||||
0.384831 | + | 0.922987i | \(0.374260\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.2426 | 1.90106 | 0.950529 | − | 0.310637i | \(-0.100542\pi\) | ||||
0.950529 | + | 0.310637i | \(0.100542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.65685 | −0.537727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.34315 | 0.263624 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.68629 | −0.291369 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.82843 | 0.303239 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.2426 | 1.50972 | 0.754858 | − | 0.655888i | \(-0.227706\pi\) | ||||
0.754858 | + | 0.655888i | \(0.227706\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.82843 | 0.293294 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.686292 | 0.0704120 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.24264 | 0.836913 | 0.418457 | − | 0.908237i | \(-0.362571\pi\) | ||||
0.418457 | + | 0.908237i | \(0.362571\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.82843 | 0.485275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.7279 | −1.46548 | −0.732742 | − | 0.680507i | \(-0.761760\pi\) | ||||
−0.732742 | + | 0.680507i | \(0.761760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.1421 | −1.39347 | −0.696733 | − | 0.717331i | \(-0.745364\pi\) | ||||
−0.696733 | + | 0.717331i | \(0.745364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.17157 | −0.693302 | −0.346651 | − | 0.937994i | \(-0.612681\pi\) | ||||
−0.346651 | + | 0.937994i | \(0.612681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3137 | −1.84992 | −0.924959 | − | 0.380067i | \(-0.875901\pi\) | ||||
−0.924959 | + | 0.380067i | \(0.875901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.65685 | −0.916588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.485281 | −0.0452527 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.24264 | −0.392232 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.75736 | 0.158456 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.3137 | −0.996116 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.585786 | −0.0504165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8284 | −1.26688 | −0.633439 | − | 0.773793i | \(-0.718357\pi\) | ||||
−0.633439 | + | 0.773793i | \(0.718357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9706 | −1.10015 | −0.550074 | − | 0.835116i | \(-0.685401\pi\) | ||||
−0.550074 | + | 0.835116i | \(0.685401\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4853 | 1.05145 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.4853 | −1.71307 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.65685 | −0.137594 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.3137 | 1.74609 | 0.873044 | − | 0.487642i | \(-0.162143\pi\) | ||||
0.873044 | + | 0.487642i | \(0.162143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.65685 | 0.134833 | 0.0674164 | − | 0.997725i | \(-0.478524\pi\) | ||||
0.0674164 | + | 0.997725i | \(0.478524\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.58579 | 0.370739 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.65685 | −0.133082 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.24264 | 0.657834 | 0.328917 | − | 0.944359i | \(-0.393316\pi\) | ||||
0.328917 | + | 0.944359i | \(0.393316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.65685 | 0.443079 | 0.221540 | − | 0.975151i | \(-0.428892\pi\) | ||||
0.221540 | + | 0.975151i | \(0.428892\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.82843 | −0.220193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.17157 | −0.709718 | −0.354859 | − | 0.934920i | \(-0.615471\pi\) | ||||
−0.354859 | + | 0.934920i | \(0.615471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.17157 | −0.0895924 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.4142 | 1.47604 | 0.738018 | − | 0.674781i | \(-0.235762\pi\) | ||||
0.738018 | + | 0.674781i | \(0.235762\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.48528 | 0.637793 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.4853 | −0.783707 | −0.391853 | − | 0.920028i | \(-0.628166\pi\) | ||||
−0.391853 | + | 0.920028i | \(0.628166\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.07107 | −0.525588 | −0.262794 | − | 0.964852i | \(-0.584644\pi\) | ||||
−0.262794 | + | 0.964852i | \(0.584644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.07107 | 0.227020 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.65685 | 0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.1421 | 1.61919 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.1421 | −1.16800 | −0.584002 | − | 0.811752i | \(-0.698514\pi\) | ||||
−0.584002 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.48528 | 0.177975 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.3137 | 1.80353 | 0.901764 | − | 0.432230i | \(-0.142273\pi\) | ||||
0.901764 | + | 0.432230i | \(0.142273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.65685 | 0.401004 | 0.200502 | − | 0.979693i | \(-0.435743\pi\) | ||||
0.200502 | + | 0.979693i | \(0.435743\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3137 | 0.798007 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.02944 | −0.0718990 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.828427 | 0.0575797 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.65685 | 0.664805 | 0.332403 | − | 0.943138i | \(-0.392141\pi\) | ||||
0.332403 | + | 0.943138i | \(0.392141\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.48528 | 0.444364 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.62742 | 0.451986 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.2426 | 1.09758 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.4558 | −1.30874 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.34315 | 0.156909 | 0.0784543 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784543 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8284 | 0.718708 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.5858 | 1.49251 | 0.746255 | − | 0.665660i | \(-0.231850\pi\) | ||||
0.746255 | + | 0.665660i | \(0.231850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.17157 | −0.600850 | −0.300425 | − | 0.953805i | \(-0.597128\pi\) | ||||
−0.300425 | + | 0.953805i | \(0.597128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.31371 | −0.477094 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.34315 | 0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.17157 | −0.463890 | −0.231945 | − | 0.972729i | \(-0.574509\pi\) | ||||
−0.231945 | + | 0.972729i | \(0.574509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.89949 | −0.380020 | −0.190010 | − | 0.981782i | \(-0.560852\pi\) | ||||
−0.190010 | + | 0.981782i | \(0.560852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.97056 | 0.316269 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.1421 | −1.39760 | −0.698800 | − | 0.715317i | \(-0.746282\pi\) | ||||
−0.698800 | + | 0.715317i | \(0.746282\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.68629 | −0.168222 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.585786 | −0.0365404 | −0.0182702 | − | 0.999833i | \(-0.505816\pi\) | ||||
−0.0182702 | + | 0.999833i | \(0.505816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.14214 | 0.502066 | 0.251033 | − | 0.967979i | \(-0.419230\pi\) | ||||
0.251033 | + | 0.967979i | \(0.419230\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17157 | −0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.2426 | 0.871635 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.8995 | 1.21329 | 0.606647 | − | 0.794971i | \(-0.292514\pi\) | ||||
0.606647 | + | 0.794971i | \(0.292514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.1421 | −1.34504 | −0.672519 | − | 0.740079i | \(-0.734788\pi\) | ||||
−0.672519 | + | 0.740079i | \(0.734788\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.4853 | −1.35591 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6274 | −0.999045 | −0.499522 | − | 0.866301i | \(-0.666491\pi\) | ||||
−0.499522 | + | 0.866301i | \(0.666491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.82843 | 0.169334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.82843 | 0.407350 | 0.203675 | − | 0.979039i | \(-0.434711\pi\) | ||||
0.203675 | + | 0.979039i | \(0.434711\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.14214 | −0.127337 | −0.0636684 | − | 0.997971i | \(-0.520280\pi\) | ||||
−0.0636684 | + | 0.997971i | \(0.520280\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.686292 | 0.0406524 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.02944 | 0.237026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.24264 | 0.483192 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2426 | 0.598381 | 0.299191 | − | 0.954193i | \(-0.403283\pi\) | ||||
0.299191 | + | 0.954193i | \(0.403283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.97056 | −0.289397 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.82843 | 0.280174 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.51472 | −0.203261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.7279 | −0.846097 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.79899 | −0.103010 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.4853 | 1.62574 | 0.812870 | − | 0.582445i | \(-0.197904\pi\) | ||||
0.812870 | + | 0.582445i | \(0.197904\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.1421 | −0.804518 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7990 | −0.895879 | −0.447939 | − | 0.894064i | \(-0.647842\pi\) | ||||
−0.447939 | + | 0.894064i | \(0.647842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.27208 | 0.184949 | 0.0924744 | − | 0.995715i | \(-0.470522\pi\) | ||||
0.0924744 | + | 0.995715i | \(0.470522\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.0000 | 1.23564 | 0.617822 | − | 0.786318i | \(-0.288015\pi\) | ||||
0.617822 | + | 0.786318i | \(0.288015\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.6569 | 0.764637 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.17157 | −0.400278 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.37258 | −0.298939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.7574 | 1.09594 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.3137 | −1.06805 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3137 | 0.841718 | 0.420859 | − | 0.907126i | \(-0.361729\pi\) | ||||
0.420859 | + | 0.907126i | \(0.361729\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.65685 | −0.529192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.62742 | −0.362094 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6569 | 1.17972 | 0.589862 | − | 0.807504i | \(-0.299182\pi\) | ||||
0.589862 | + | 0.807504i | \(0.299182\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0000 | −0.543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.6569 | 0.739560 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.485281 | −0.0261267 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.4853 | −0.777611 | −0.388805 | − | 0.921320i | \(-0.627112\pi\) | ||||
−0.388805 | + | 0.921320i | \(0.627112\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.4142 | −0.718046 | −0.359023 | − | 0.933329i | \(-0.616890\pi\) | ||||
−0.359023 | + | 0.933329i | \(0.616890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.24264 | −0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.6985 | 1.68714 | 0.843570 | − | 0.537019i | \(-0.180450\pi\) | ||||
0.843570 | + | 0.537019i | \(0.180450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.79899 | −0.201629 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1716 | 1.22295 | 0.611474 | − | 0.791264i | \(-0.290577\pi\) | ||||
0.611474 | + | 0.791264i | \(0.290577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6274 | −0.927759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.3137 | 0.646302 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.51472 | −0.498023 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3137 | 1.42576 | 0.712882 | − | 0.701284i | \(-0.247390\pi\) | ||||
0.712882 | + | 0.701284i | \(0.247390\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.75736 | 0.0914845 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.3137 | 0.896470 | 0.448235 | − | 0.893916i | \(-0.352053\pi\) | ||||
0.448235 | + | 0.893916i | \(0.352053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.686292 | 0.0352524 | 0.0176262 | − | 0.999845i | \(-0.494389\pi\) | ||||
0.0176262 | + | 0.999845i | \(0.494389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.0000 | 1.02463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.9706 | 1.27594 | 0.637968 | − | 0.770063i | \(-0.279775\pi\) | ||||
0.637968 | + | 0.770063i | \(0.279775\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.3137 | −0.575108 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.79899 | −0.192616 | −0.0963082 | − | 0.995352i | \(-0.530703\pi\) | ||||
−0.0963082 | + | 0.995352i | \(0.530703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.79899 | 0.192123 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.37258 | −0.0690621 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.75736 | 0.389331 | 0.194665 | − | 0.980870i | \(-0.437638\pi\) | ||||
0.194665 | + | 0.980870i | \(0.437638\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.82843 | 0.340995 | 0.170498 | − | 0.985358i | \(-0.445462\pi\) | ||||
0.170498 | + | 0.985358i | \(0.445462\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0000 | −0.597763 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.585786 | −0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −46.6274 | −2.31124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.242641 | 0.0119978 | 0.00599890 | − | 0.999982i | \(-0.498090\pi\) | ||||
0.00599890 | + | 0.999982i | \(0.498090\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.8284 | −0.731432 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.34315 | −0.115021 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.9706 | −0.635171 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.4853 | −1.19618 | −0.598092 | − | 0.801427i | \(-0.704074\pi\) | ||||
−0.598092 | + | 0.801427i | \(0.704074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.68629 | 0.130922 | 0.0654609 | − | 0.997855i | \(-0.479148\pi\) | ||||
0.0654609 | + | 0.997855i | \(0.479148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.4853 | 0.607055 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.3553 | −1.03589 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.4853 | −0.989039 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.1421 | 0.970213 | 0.485106 | − | 0.874455i | \(-0.338781\pi\) | ||||
0.485106 | + | 0.874455i | \(0.338781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.0711 | 0.724269 | 0.362135 | − | 0.932126i | \(-0.382048\pi\) | ||||
0.362135 | + | 0.932126i | \(0.382048\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.65685 | −0.0794401 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.970563 | −0.0464283 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.3137 | 1.68543 | 0.842716 | − | 0.538359i | \(-0.180956\pi\) | ||||
0.842716 | + | 0.538359i | \(0.180956\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.8284 | 0.799543 | 0.399771 | − | 0.916615i | \(-0.369090\pi\) | ||||
0.399771 | + | 0.916615i | \(0.369090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.34315 | −0.395503 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.3137 | 1.00810 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.6274 | 1.35101 | 0.675506 | − | 0.737355i | \(-0.263925\pi\) | ||||
0.675506 | + | 0.737355i | \(0.263925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.48528 | 0.399556 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.65685 | 0.0778458 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6274 | 0.964910 | 0.482455 | − | 0.875921i | \(-0.339745\pi\) | ||||
0.482455 | + | 0.875921i | \(0.339745\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.58579 | 0.214046 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.3848 | 0.949414 | 0.474707 | − | 0.880144i | \(-0.342554\pi\) | ||||
0.474707 | + | 0.880144i | \(0.342554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.65685 | −0.448792 | −0.224396 | − | 0.974498i | \(-0.572041\pi\) | ||||
−0.224396 | + | 0.974498i | \(0.572041\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.65685 | −0.0768348 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1716 | 0.609508 | 0.304754 | − | 0.952431i | \(-0.401426\pi\) | ||||
0.304754 | + | 0.952431i | \(0.401426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.24264 | 0.379801 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −54.6274 | −2.51177 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.45584 | 0.250331 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.1716 | 0.784589 | 0.392295 | − | 0.919840i | \(-0.371681\pi\) | ||||
0.392295 | + | 0.919840i | \(0.371681\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.9706 | 1.86810 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.82843 | −0.219248 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.9706 | −1.31278 | −0.656391 | − | 0.754421i | \(-0.727918\pi\) | ||||
−0.656391 | + | 0.754421i | \(0.727918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.65685 | 0.255812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8284 | −1.12049 | −0.560246 | − | 0.828327i | \(-0.689293\pi\) | ||||
−0.560246 | + | 0.828327i | \(0.689293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.9706 | 0.584165 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.82843 | −0.127128 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.97056 | −0.401578 | −0.200789 | − | 0.979635i | \(-0.564350\pi\) | ||||
−0.200789 | + | 0.979635i | \(0.564350\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.17157 | −0.409756 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.31371 | 0.147751 | 0.0738755 | − | 0.997267i | \(-0.476463\pi\) | ||||
0.0738755 | + | 0.997267i | \(0.476463\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.62742 | 0.383915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.384776 | −0.0170549 | −0.00852746 | − | 0.999964i | \(-0.502714\pi\) | ||||
−0.00852746 | + | 0.999964i | \(0.502714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.17157 | −0.0517262 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.28427 | 0.365049 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 60.2843 | 2.65130 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.4142 | 0.852189 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.75736 | 0.252234 | 0.126117 | − | 0.992015i | \(-0.459748\pi\) | ||||
0.126117 | + | 0.992015i | \(0.459748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.9706 | −1.26679 | −0.633397 | − | 0.773827i | \(-0.718340\pi\) | ||||
−0.633397 | + | 0.773827i | \(0.718340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9706 | 0.565007 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.48528 | 0.368230 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.45584 | −0.322948 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.20101 | 0.181626 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.4853 | −0.452473 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.0000 | 0.773880 | 0.386940 | − | 0.922105i | \(-0.373532\pi\) | ||||
0.386940 | + | 0.922105i | \(0.373532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.07107 | −0.303449 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.3137 | 0.484626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.9706 | 1.58075 | 0.790374 | − | 0.612625i | \(-0.209886\pi\) | ||||
0.790374 | + | 0.612625i | \(0.209886\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.07107 | 0.131070 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.31371 | −0.141169 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.65685 | 0.240120 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.6274 | 0.535041 | 0.267520 | − | 0.963552i | \(-0.413796\pi\) | ||||
0.267520 | + | 0.963552i | \(0.413796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.0000 | 2.03018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.1421 | 0.934842 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.1421 | −1.27034 | −0.635170 | − | 0.772373i | \(-0.719070\pi\) | ||||
−0.635170 | + | 0.772373i | \(0.719070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.85786 | 0.246442 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.1421 | −1.43131 | −0.715656 | − | 0.698453i | \(-0.753872\pi\) | ||||
−0.715656 | + | 0.698453i | \(0.753872\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.3431 | 1.26982 | 0.634911 | − | 0.772586i | \(-0.281037\pi\) | ||||
0.634911 | + | 0.772586i | \(0.281037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.1421 | −0.674347 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.85786 | −0.160884 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.2132 | −1.21616 | −0.608081 | − | 0.793875i | \(-0.708060\pi\) | ||||
−0.608081 | + | 0.793875i | \(0.708060\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.00000 | 0.0831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.65685 | 0.399946 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.48528 | 0.102754 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.79899 | −0.156801 | −0.0784005 | − | 0.996922i | \(-0.524981\pi\) | ||||
−0.0784005 | + | 0.996922i | \(0.524981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.31371 | −0.136539 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.3137 | 1.04127 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.5858 | 1.83092 | 0.915459 | − | 0.402410i | \(-0.131827\pi\) | ||||
0.915459 | + | 0.402410i | \(0.131827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.65685 | 0.231520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.4558 | −1.12182 | −0.560908 | − | 0.827878i | \(-0.689548\pi\) | ||||
−0.560908 | + | 0.827878i | \(0.689548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.75736 | −0.153266 | −0.0766329 | − | 0.997059i | \(-0.524417\pi\) | ||||
−0.0766329 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3137 | 0.460730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.21320 | −0.293258 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.97056 | −0.364104 | −0.182052 | − | 0.983289i | \(-0.558274\pi\) | ||||
−0.182052 | + | 0.983289i | \(0.558274\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −52.9706 | −2.14296 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6569 | 0.874712 | 0.437356 | − | 0.899288i | \(-0.355915\pi\) | ||||
0.437356 | + | 0.899288i | \(0.355915\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.02944 | −0.0415109 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.4853 | 0.502639 | 0.251319 | − | 0.967904i | \(-0.419136\pi\) | ||||
0.251319 | + | 0.967904i | \(0.419136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.3431 | −0.898047 | −0.449023 | − | 0.893520i | \(-0.648228\pi\) | ||||
−0.449023 | + | 0.893520i | \(0.648228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.828427 | 0.0332436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.65685 | −0.225913 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.2843 | −1.76573 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.9706 | −1.47177 | −0.735887 | − | 0.677104i | \(-0.763235\pi\) | ||||
−0.735887 | + | 0.677104i | \(0.763235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.65685 | 0.383825 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.7157 | −0.464925 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.48528 | 0.256554 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.1127 | −1.07089 | −0.535444 | − | 0.844571i | \(-0.679856\pi\) | ||||
−0.535444 | + | 0.844571i | \(0.679856\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.79899 | 0.307562 | 0.153781 | − | 0.988105i | \(-0.450855\pi\) | ||||
0.153781 | + | 0.988105i | \(0.450855\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.62742 | 0.260954 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.7990 | −1.56466 | −0.782330 | − | 0.622864i | \(-0.785969\pi\) | ||||
−0.782330 | + | 0.622864i | \(0.785969\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.9706 | 1.60824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.8579 | −0.698832 | −0.349416 | − | 0.936968i | \(-0.613620\pi\) | ||||
−0.349416 | + | 0.936968i | \(0.613620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.34315 | −0.0915543 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.2426 | 0.633686 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.4853 | −1.49917 | −0.749587 | − | 0.661906i | \(-0.769748\pi\) | ||||
−0.749587 | + | 0.661906i | \(0.769748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0711 | −0.741779 | −0.370889 | − | 0.928677i | \(-0.620947\pi\) | ||||
−0.370889 | + | 0.928677i | \(0.620947\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.4558 | −0.755602 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.34315 | 0.0907270 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.34315 | 0.0905912 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.8284 | 0.572445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.686292 | −0.0264546 | −0.0132273 | − | 0.999913i | \(-0.504211\pi\) | ||||
−0.0132273 | + | 0.999913i | \(0.504211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.65685 | −0.179242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.6985 | 1.21827 | 0.609136 | − | 0.793066i | \(-0.291516\pi\) | ||||
0.609136 | + | 0.793066i | \(0.291516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.8284 | 0.414946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.7990 | −1.44634 | −0.723169 | − | 0.690671i | \(-0.757315\pi\) | ||||
−0.723169 | + | 0.690671i | \(0.757315\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.68629 | 0.331886 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.5858 | 0.861701 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.48528 | −0.323263 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.3137 | −1.19123 | −0.595615 | − | 0.803270i | \(-0.703092\pi\) | ||||
−0.595615 | + | 0.803270i | \(0.703092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.59798 | 0.288208 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.05887 | 0.305252 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.17157 | −0.346901 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.1421 | −0.836297 | −0.418148 | − | 0.908379i | \(-0.637321\pi\) | ||||
−0.418148 | + | 0.908379i | \(0.637321\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3137 | 0.426705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.31371 | −0.275450 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.6274 | 1.45068 | 0.725342 | − | 0.688389i | \(-0.241682\pi\) | ||||
0.725342 | + | 0.688389i | \(0.241682\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.34315 | 0.0878748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.34315 | 0.0877515 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.17157 | −0.267827 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.6274 | 1.44056 | 0.720280 | − | 0.693684i | \(-0.244013\pi\) | ||||
0.720280 | + | 0.693684i | \(0.244013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.89949 | −0.219405 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.1716 | −0.489180 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.1421 | −1.41461 | −0.707307 | − | 0.706907i | \(-0.750090\pi\) | ||||
−0.707307 | + | 0.706907i | \(0.750090\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51.8823 | −1.91893 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.0416 | −1.47897 | −0.739486 | − | 0.673172i | \(-0.764931\pi\) | ||||
−0.739486 | + | 0.673172i | \(0.764931\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.6274 | 2.01223 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.970563 | 0.0357027 | 0.0178514 | − | 0.999841i | \(-0.494317\pi\) | ||||
0.0178514 | + | 0.999841i | \(0.494317\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.97056 | 0.182598 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.828427 | 0.0303920 | 0.0151960 | − | 0.999885i | \(-0.495163\pi\) | ||||
0.0151960 | + | 0.999885i | \(0.495163\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.4853 | −0.457425 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2843 | −1.32403 | −0.662016 | − | 0.749490i | \(-0.730299\pi\) | ||||
−0.662016 | + | 0.749490i | \(0.730299\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.1421 | −0.806904 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.970563 | −0.0353224 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.9411 | 0.942846 | 0.471423 | − | 0.881907i | \(-0.343740\pi\) | ||||
0.471423 | + | 0.881907i | \(0.343740\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.1005 | −0.438643 | −0.219321 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219321 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.68629 | −0.0971231 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.0000 | −1.29988 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8701 | −0.680472 | −0.340236 | − | 0.940340i | \(-0.610507\pi\) | ||||
−0.340236 | + | 0.940340i | \(0.610507\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.585786 | −0.0210966 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.3553 | 1.34358 | 0.671789 | − | 0.740742i | \(-0.265526\pi\) | ||||
0.671789 | + | 0.740742i | \(0.265526\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.1716 | −0.473137 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.05887 | −0.0737668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.3137 | 1.12049 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.82843 | 0.101080 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.82843 | −0.172334 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.31371 | 0.260706 | 0.130353 | − | 0.991468i | \(-0.458389\pi\) | ||||
0.130353 | + | 0.991468i | \(0.458389\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.14214 | 0.289868 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0294 | −0.462689 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.17157 | −0.0415514 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.5858 | 1.29594 | 0.647968 | − | 0.761668i | \(-0.275619\pi\) | ||||
0.647968 | + | 0.761668i | \(0.275619\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 57.2548 | 2.02553 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.2426 | 0.503239 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 78.4264 | 2.76761 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.8995 | 0.700495 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.6274 | 1.42838 | 0.714192 | − | 0.699950i | \(-0.246794\pi\) | ||||
0.714192 | + | 0.699950i | \(0.246794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3431 | −0.503656 | −0.251828 | − | 0.967772i | \(-0.581032\pi\) | ||||
−0.251828 | + | 0.967772i | \(0.581032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.1421 | −0.776559 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.31371 | −0.116074 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.2548 | 0.463728 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.3137 | 1.16266 | 0.581328 | − | 0.813669i | \(-0.302533\pi\) | ||||
0.581328 | + | 0.813669i | \(0.302533\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.97056 | 0.312694 | 0.156347 | − | 0.987702i | \(-0.450028\pi\) | ||||
0.156347 | + | 0.987702i | \(0.450028\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.4853 | −0.782837 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8579 | −0.412338 | −0.206169 | − | 0.978516i | \(-0.566100\pi\) | ||||
−0.206169 | + | 0.978516i | \(0.566100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.38478 | 0.0828267 | 0.0414134 | − | 0.999142i | \(-0.486814\pi\) | ||||
0.0414134 | + | 0.999142i | \(0.486814\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.6274 | −0.576799 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.37258 | 0.185926 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.82843 | 0.0977647 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7990 | −0.545442 | −0.272721 | − | 0.962093i | \(-0.587924\pi\) | ||||
−0.272721 | + | 0.962093i | \(0.587924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.82843 | 0.235184 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.92893 | −0.100758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.14214 | −0.0735179 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0711 | −0.652981 | −0.326490 | − | 0.945200i | \(-0.605866\pi\) | ||||
−0.326490 | + | 0.945200i | \(0.605866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.686292 | 0.0234707 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.2132 | 1.06622 | 0.533111 | − | 0.846045i | \(-0.321023\pi\) | ||||
0.533111 | + | 0.846045i | \(0.321023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.4558 | −1.82389 | −0.911945 | − | 0.410313i | \(-0.865420\pi\) | ||||
−0.911945 | + | 0.410313i | \(0.865420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.0833 | −1.43253 | −0.716265 | − | 0.697828i | \(-0.754150\pi\) | ||||
−0.716265 | + | 0.697828i | \(0.754150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3726 | −0.386679 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.02944 | 0.136847 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3137 | 0.383791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.24264 | 0.278971 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.2843 | −0.955092 | −0.477546 | − | 0.878607i | \(-0.658474\pi\) | ||||
−0.477546 | + | 0.878607i | \(0.658474\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.2426 | 0.345476 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0416 | −0.607838 | −0.303919 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303919 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.6569 | 0.728811 | 0.364406 | − | 0.931240i | \(-0.381272\pi\) | ||||
0.364406 | + | 0.931240i | \(0.381272\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.97056 | −0.167084 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.201010 | −0.00674926 | −0.00337463 | − | 0.999994i | \(-0.501074\pi\) | ||||
−0.00337463 | + | 0.999994i | \(0.501074\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.82843 | 0.161758 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.6274 | −0.489488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.14214 | 0.205309 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.51472 | −0.117353 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.00000 | 0.266815 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.17157 | 0.305549 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.14214 | 0.137689 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.3431 | −1.40598 | −0.702991 | − | 0.711199i | \(-0.748152\pi\) | ||||
−0.702991 | + | 0.711199i | \(0.748152\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.7279 | −0.488494 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4853 | −0.347393 | −0.173696 | − | 0.984799i | \(-0.555571\pi\) | ||||
−0.173696 | + | 0.984799i | \(0.555571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.3137 | 0.639190 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.79899 | −0.0594728 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.68629 | 0.286534 | 0.143267 | − | 0.989684i | \(-0.454239\pi\) | ||||
0.143267 | + | 0.989684i | \(0.454239\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.4853 | 0.938622 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.5147 | −0.905658 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.9706 | 1.47862 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.1421 | −0.464489 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.89949 | 0.127938 | 0.0639691 | − | 0.997952i | \(-0.479624\pi\) | ||||
0.0639691 | + | 0.997952i | \(0.479624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.7990 | −0.517236 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.9706 | −0.424183 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.3553 | −0.632311 | −0.316156 | − | 0.948707i | \(-0.602392\pi\) | ||||
−0.316156 | + | 0.948707i | \(0.602392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.27208 | 0.106780 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.7279 | −0.349720 | −0.174860 | − | 0.984593i | \(-0.555947\pi\) | ||||
−0.174860 | + | 0.984593i | \(0.555947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.45584 | 0.0474088 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.7696 | −0.479946 | −0.239973 | − | 0.970780i | \(-0.577139\pi\) | ||||
−0.239973 | + | 0.970780i | \(0.577139\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −68.9117 | −2.23697 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0000 | 0.713399 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.45584 | 0.305984 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.6569 | 0.441463 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.17157 | −0.231101 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.17157 | −0.0377143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.68629 | −0.279332 | −0.139666 | − | 0.990199i | \(-0.544603\pi\) | ||||
−0.139666 | + | 0.990199i | \(0.544603\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.37258 | −0.172592 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.7574 | 0.632742 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.7990 | 1.01734 | 0.508670 | − | 0.860962i | \(-0.330137\pi\) | ||||
0.508670 | + | 0.860962i | \(0.330137\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.7696 | 2.19788 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.3137 | −0.616639 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.6274 | 1.48718 | 0.743592 | − | 0.668634i | \(-0.233121\pi\) | ||||
0.743592 | + | 0.668634i | \(0.233121\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.8284 | −0.472473 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.37258 | −0.298031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.6274 | 0.845848 | 0.422924 | − | 0.906165i | \(-0.361004\pi\) | ||||
0.422924 | + | 0.906165i | \(0.361004\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.3137 | 0.485966 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.31371 | −0.105052 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.6152 | 0.557880 | 0.278940 | − | 0.960309i | \(-0.410017\pi\) | ||||
0.278940 | + | 0.960309i | \(0.410017\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.65685 | −0.305529 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9408.2.a.dv.1.2 | 2 | ||
4.3 | odd | 2 | 9408.2.a.dh.1.2 | 2 | |||
7.6 | odd | 2 | 9408.2.a.dr.1.1 | 2 | |||
8.3 | odd | 2 | 2352.2.a.bg.1.1 | 2 | |||
8.5 | even | 2 | 1176.2.a.l.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 3528.2.a.bc.1.2 | 2 | |||
24.11 | even | 2 | 7056.2.a.ce.1.2 | 2 | |||
28.27 | even | 2 | 9408.2.a.ed.1.1 | 2 | |||
56.3 | even | 6 | 2352.2.q.bg.961.1 | 4 | |||
56.5 | odd | 6 | 1176.2.q.m.361.1 | 4 | |||
56.11 | odd | 6 | 2352.2.q.ba.961.2 | 4 | |||
56.13 | odd | 2 | 1176.2.a.m.1.2 | yes | 2 | ||
56.19 | even | 6 | 2352.2.q.bg.1537.1 | 4 | |||
56.27 | even | 2 | 2352.2.a.z.1.2 | 2 | |||
56.37 | even | 6 | 1176.2.q.n.361.2 | 4 | |||
56.45 | odd | 6 | 1176.2.q.m.961.1 | 4 | |||
56.51 | odd | 6 | 2352.2.q.ba.1537.2 | 4 | |||
56.53 | even | 6 | 1176.2.q.n.961.2 | 4 | |||
168.5 | even | 6 | 3528.2.s.bc.361.2 | 4 | |||
168.53 | odd | 6 | 3528.2.s.bl.3313.1 | 4 | |||
168.83 | odd | 2 | 7056.2.a.cw.1.1 | 2 | |||
168.101 | even | 6 | 3528.2.s.bc.3313.2 | 4 | |||
168.125 | even | 2 | 3528.2.a.bm.1.1 | 2 | |||
168.149 | odd | 6 | 3528.2.s.bl.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.l.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
1176.2.a.m.1.2 | yes | 2 | 56.13 | odd | 2 | ||
1176.2.q.m.361.1 | 4 | 56.5 | odd | 6 | |||
1176.2.q.m.961.1 | 4 | 56.45 | odd | 6 | |||
1176.2.q.n.361.2 | 4 | 56.37 | even | 6 | |||
1176.2.q.n.961.2 | 4 | 56.53 | even | 6 | |||
2352.2.a.z.1.2 | 2 | 56.27 | even | 2 | |||
2352.2.a.bg.1.1 | 2 | 8.3 | odd | 2 | |||
2352.2.q.ba.961.2 | 4 | 56.11 | odd | 6 | |||
2352.2.q.ba.1537.2 | 4 | 56.51 | odd | 6 | |||
2352.2.q.bg.961.1 | 4 | 56.3 | even | 6 | |||
2352.2.q.bg.1537.1 | 4 | 56.19 | even | 6 | |||
3528.2.a.bc.1.2 | 2 | 24.5 | odd | 2 | |||
3528.2.a.bm.1.1 | 2 | 168.125 | even | 2 | |||
3528.2.s.bc.361.2 | 4 | 168.5 | even | 6 | |||
3528.2.s.bc.3313.2 | 4 | 168.101 | even | 6 | |||
3528.2.s.bl.361.1 | 4 | 168.149 | odd | 6 | |||
3528.2.s.bl.3313.1 | 4 | 168.53 | odd | 6 | |||
7056.2.a.ce.1.2 | 2 | 24.11 | even | 2 | |||
7056.2.a.cw.1.1 | 2 | 168.83 | odd | 2 | |||
9408.2.a.dh.1.2 | 2 | 4.3 | odd | 2 | |||
9408.2.a.dr.1.1 | 2 | 7.6 | odd | 2 | |||
9408.2.a.dv.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9408.2.a.ed.1.1 | 2 | 28.27 | even | 2 |